Re: Specifying Sets

Chris Menzel wrote:
On Thu, 13 Nov 2008 19:55:03 +0000, John Jones <jonescardiff@xxxxxxx>
said:
Chris Menzel wrote:
...
Indeed, in ordinary discourse, "set" is entirely ambiguous. This is
hardly news, and it is not of the least significance for mathematics.
"1) The method of enumeration lists the contents or objects of the set
{The President of the United States, Donald Rumsfeld, 2005}
2) The method of description states what condition must be satisified for something to be a member of the set. {x: x is blond}: the set of all x such that x is blond, or the set of all blonds."

If you reread that, it is plain that the intention was to read 'list' in much the same way as we read a shopping list, ie. unordered. I got that quote from a logical encyclopaedia.
You may well have -- though I'd be curious what "logical encyclopedia"
this is from. Be that as it may, all you've done is illustrate that
point that "set" and "list" don't have precise meanings in ordinary
language -- you do recognize that the above is just an ordinary language
use of "list", right, and not a mathematical definition of the term?
The term list used in the quote is different from the list you claim
is used by mathematics.

Indeed, it is just an ordinary language use.

What is the mathematical term for the list as it is used in the quote?

The list? There is no list referred to in the quote. "list" is being
used as a verb there. The example given is of a set, whose elements we
can list as follows: The President of the United States, Donald
Rumsfeld, 2005.

Just use that.

There is no that to use.

Here's the quote. Note the term 'list'. God, you are boring.

"There are two methods of specifying the contents of a set.
1) The method of enumeration lists the contents or objects of the set
{The President of the United States, Donald Rumsfeld, 2005}
2) The method of description states what condition must be satisified for something to be a member of the set. {x: x is blond}: the set of all x such that x is blond, or the set of all blonds. "

And that, moreover, it is not even talking about lists, just about
two different informal ways of picking out a set?
The list in the quote doesn't pick out a set,

Again, there is no list in the quote.

See above. Crikey mate. You're a bit of an effort.

A set is referred to in the
quote, one whose elements can be listed as above; or any permutation
thereof.

Permutation? What 'permutation'? Are you calling the effort you made in 'making it up as you go along' a bona fide objection?

informally or formally, or anything that could be considered being
called a set.

You don't think there is a set containing Bush, Rumsfeld, and the number
2005?

Of course not! A set of what? You have merely listed objects. You haven't even listed three objects because they haven't been counted.

The trap is to think that where the word 'set' is used, we have a new
property, or something substantive, but we don't. A list and 'all'
didn't pick out a 'set' in the quoted material, despite the fact that
the author thought that they did.

There you go again,

again

just makin' crazy, incomprehensible stuff up instead
of cracking a book.

book.

Ah, well, then, no wonder you refuse actually to learn

learn.

any

any

mathematics:
you think

too late

our present day mathematics is fundamentally confused

confused

and the
task falls

falls

to you

me

to rethink all 2000+ years from the ground up


up

Well,
good luck to you, sir! You've made an impressive start!

Thank-you. Now then, what's the cure for intermittent loose stools?



.

Relevant Pages

  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... x such that x is blond, or the set of all blonds. ... Donald Rumsfeld, 2005}, we ought to write 'The President of the United ... There's no reason why the objects in a set can't be looked at as lists ...
    (sci.logic)
  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... x such that x is blond, or the set of all blonds. ... Donald Rumsfeld, 2005}, we ought to write 'The President of the United ... There's no reason why the objects in a set can't be looked at as lists ...
    (sci.logic)
  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... The term list used in the quote is different from the list you claim ... The President of the United States, ... The method of enumeration lists the contents or objects of the set ...
    (sci.logic)
  • Re: Specifying Sets
    ... {The President of the United States, Donald Rumsfeld, 2005} ... The term list used in the quote is different from the list you claim ... The President of the United States, ... The method of enumeration lists the contents or objects of the set ...
    (sci.logic)
  • Re: newbie Q: opposite of quote
    ... (eval (quote a)) ... a first Common Lisp lesson. ... you can use lists as short as you want. ... symbols, set, setq, setf, psetq, psetf. ...
    (comp.lang.lisp)
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